Photovoltaic, wind power and other renewable energy sources are connected to the power grid on a large scale, gradually replacing the traditional synchronous generators, resulting in a continuous decline in the inertia and damping level. This threatens the safe and stable operation of the grid. In response to this problem, a composite inertia-damping-impedance emulation control (IDIE) scheme based on a supercapacitor is proposed. By combining the swing equation, the power transmission equation of a synchronous generator and the power dynamic equation of a supercapacitor, a core algorithm is designed to control the active power of the supercapacitor to emulate the physical properties of the synchronous generator rotating mass, damping winding and winding impedance. The key parameters of the scheme are also optimized by small signal stability analysis. Finally, the IDIE scheme is evaluated in various transient conditions based on the controller-hardware-in-the-loop test. The results show that the IDIE scheme can ensure frequency stability and support the dynamic operation of the grid by configuring and optimizing simulated damping and impedance and flexibly simulating the inertia of the synchronous generator at the same time.